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Integral formulas for recovering extremal measures for vector constrained energy problems. (English) Zbl 1434.31003
Summary: Extremal problems for vector potentials have wide applications in asymptotic analysis of Hermite-Padé approximants of analytic functions. We consider equilibrium vector logarithmic potentials with constrains on measures. We study the dependance of the supports of the equilibrium measures on their masses. We obtain the integral formulas for recovering the extremal measure of given mass from the supports of the equilibrium measures of smaller masses.
MSC:
31A15 Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions
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